306 PROCEEDINGS OF THE AMERICAN ACADEMY. 



Zenneck,!" in 1904, obtained further experimental proof of the 

 approximately linear damping due to a spark gap. He photographed 

 the line deflection, and by a process of projection from the several 

 brighter spots, due to the decreasing amplitudes of the oscillations, de- 

 rived the damping curves. Frequencies up to 1800 per second were 

 used by him, 



Heydweiller,!! in 1906, showed that the results obtained by the 

 above mentioned experimenters can be deducted theoretically. Hey- 

 dweiller assumes, in deducing the linear damping, that the gap has a 

 characteristic expressible in the form. 



b 



e = a + . 



t 



where e and ^ are the voltage across and current thi'ongh the gap, re- 

 spectively, and a and b are constants. He further assumes that b is 

 negligible, which reduces the conditions to the assumption of a con- 

 stant voltage across the gap. Solving the differential equation for the 

 discharge of a condenser across a constant potential gap, he obtained 

 rectilinear damping. 



If a discharge gap be substituted for the secondary resistance in the 

 arrangement of circuits which was used in the last section for obtain- 

 ing plain resistance damping, very clear oscillograms can be obtained 

 of the oscillation trains when the damping is caused by a gap. Al- 

 though the inherent irregularity of some metallic gaps, when used in 

 the secondary circuit, causes some irregularity of the oscillographs, yet 

 good photogi'aphic records can be obtained, as is shown by the cuts of 

 Plates 6 and 7. In order to obtain a potential sufficient to maintain 

 the discharge across the secondary gap, it was necessary to use a large 



N 

 primary condenser and supply current, and to make the ratio, -^, 



of the secondary to primary turns on the helix large. 



Cuts b and c of Plate 6 show two of the pictures first taken, and 

 illustrate well the linear damping. The gap length was very short ; 

 the terminals were of aluminum. 



Further investigation showed that the oscillation train took on en- 

 tirely different aspects according as the discharge could be classed 

 as a pure arc, or a spa?^k discharge. When the discharge is a pure arc, 

 the separate oscillations are regular and practically sinusoidal, and the 

 damping is still linear. If the discharge is classed as a spark discharge, 



" J. Zcnneck, Ann. d. Phys., 13, S22, 1904. 



" R. Heydweiller, Ann. d. Physik., 19, 646, 1906. 



